# Are there examples of compact infinite dimensional manifolds? [closed]

Are there known examples of compact infinite dimensional manifolds?

The word "manifold" is important.

• How do you define an infinite dimensional manifold? Is it modelled on the countable product of lines? – Igor Belegradek Oct 25 '13 at 0:56
• If this is your definition, then the answer is no, because if $K$ is a compact subset of a manifold $Y$ modelled on the countable product of lines, then $Y$ and $Y-K$ are homeomorphic. – Igor Belegradek Oct 25 '13 at 1:04
• just modelled on a vector space. like Banach manifold, Frechet manifold. – user8991 Oct 25 '13 at 1:07
• Any separable Frechet (or Banach) space is homeomorphic to the countable product of lines, so my answer above applies. – Igor Belegradek Oct 25 '13 at 1:18
• It seems to me Pietro Majer already addressed this in his answer here: mathoverflow.net/a/143737/2926 Right? – Todd Trimble Oct 25 '13 at 2:01